Question

Maria has a business designing and making custom T-shirts. Her cost for materials, in thousands of dollars, is given by M(t)=−3 t 2 +36t M ( t ) = − 3 t 2 + 36 t , where t t is the number of the month (1-12) on the last day of the month. Her income from sales is given by S(t)=−4 t 2 +48t S ( t ) = − 4 t 2 + 48 t . What is the function P(t) P ( t ) that gives her profit as a function of time? Hint: Profit equals the difference of the income and the cost.

Answer 1

Answer:

$P(t) = -t^2 + 12t$

Step-by-step explanation:

Given

$M(t) = -3t^2 + 36t$ -- Cost

$S(t) = -4t^2 + 48t$ --- Income

Required

Determine P(t)

P(t) is calculated as:

$P(t) = Income - Cost$

$P(t) = S(t) - M(t)$

$P(t) = -4t^2 + 48t -(-3t^2 + 36t)$

Open bracket

$P(t) = -4t^2 + 48t +3t^2 - 36t$

Collect Like Terms

$P(t) = 3t^2 -4t^2 + 48t- 36t$

$P(t) = -t^2 + 12t$